Question

17. If P(1, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then. (a) a =2,b= A
(b) a = 3,b=4
(c) a = 2, b=3
(d) a = 3, b=5​

Answer 1

Step-by-step explanation:

First we will find the mid point of the diagonal PR and SB. Let the mid point of the diagonals be O(x,y). Since, value of point P and R are given.

Therefore,

Ox= 1+5/2= 3

Oy= 2+7/2= 9/2

O(3,9/2)

Now, for the value of a

3= 4+9/2

6=4+a

6-4= a

a= 2

similarly, for the value of b

9/2= 6+b/2

9-6= b

b= 3

Hence, the coordinates of point S will be (2,3).

CORRECT ANSWER:- option(c)- a=2,b=3

hope it helps